Hematite-based photoanodes with manganese, cobalt, and nickel additives

ABSTRACT

A photoanode, photochemical cell and methods of making are disclosed. The photoanode includes an electrode at least partially formed of hematite and having a surface doped with at least one of nickel, cobalt and manganese. The electrode surface may be doped with nickel. The surface may be doped with cobalt. The electrode surface may be doped with manganese. An aqueous solution may surround the photoanode and a cathode, the photoanode being configured to generate holes upon light absorption and the cathode being configured to emit electrons to the aqueous solution. A voltage source may be electrically coupled between the photoanode and the cathode.

CROSS-REFERENCE TO PRIOR FILED APPLICATIONS

This application claims priority to earlier filed provisional application 61/554,287 filed on Nov. 1, 2011 which is incorporated herein in its entirety.

UNITED STATES GOVERNMENT RIGHTS

This invention was made with government support under Grant No. FA9550-10-1-0162 awarded by the U.S. Air Force Office of Scientific Research (AFOSR) and Grant No. DE-SC0002120 awarded by the Department of Energy. The government has certain rights in this invention.

FIELD OF INVENTION

The present invention relates to photoanodes. More particularly, it relates to high efficiency photoanodes with reduced overpotential.

BACKGROUND

In photocatalysis, sunlight is used to provide energy for endothermic chemical reactions and the energy is stored as chemical energy in the reaction products. For example, consider the water splitting reaction of H₂O→H2+O2. Among many potential candidates for use as photoanodes, hematite (α-Fe₂O₃) stands out as being cheap, abundant, and non-toxic, with a close to optimum band gap. However, it has been shown experimentally that the use of hematite as a photoanode requires a large overpotential and exhibits low efficiency. It would be desirable to provide improved photoanode compositions and methods of making such photoanodes.

SUMMARY OF THE INVENTION

A photoanode, photochemical cell and methods of making are disclosed. The photoanode includes an electrode at least partially formed of hematite and having a surface doped with at least one of nickel, cobalt and manganese. The electrode surface may be doped with nickel. The electrode surface may be doped with cobalt. The electrode surface may be doped with manganese. The electrode may be bulk doped with at least one of cobalt and nickel to enhance light absorption. The electrode may be bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport. An aqueous solution may surround the photoanode and a cathode, the photoanode being configured to generate holes upon light absorption and the cathode being configured to emit electrons to the aqueous solution.

A photochemical cell is also disclosed, the photochemical cell is configured for electrolysis of water and includes a photoanode comprised of hematite and having a surface doped with at least one of nickel, cobalt and manganese configured for immersion in the water. The photochemical cell also includes a cathode electrically coupled to the photoanode, the cathode being configured for immersion in the water. The electrode surface may be doped with nickel. The electrode surface may be doped with cobalt. The electrode surface may be doped with manganese. The electrode may be bulk doped with at least one of cobalt and nickel to enhance light absorption. The electrode may be bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport. The photoanode may be configured to generate holes upon light absorption and the cathode may be configured to emit electrons to the aqueous solution. A voltage source may be electrically coupled between the photoanode and the cathode.

A method of making a photoanode is also disclosed. The method includes, providing an electrode at least partially formed of hematite and doping a surface of the electrode with at least one of nickel, cobalt and manganese. The electrode surface may be doped with nickel. The electrode surface may be doped with cobalt. The electrode surface may be doped with manganese. The electrode may be bulk doped with at least one of cobalt and nickel to enhance light absorption. The electrode may be bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport. An aqueous solution may surround the photoanode and a cathode, the photoanode being configured to generate holes upon light absorption and the cathode being configured to emit electrons to the aqueous solution. A voltage source may be electrically coupled between the photoanode and the cathode.

A method of making a photochemical cell configured for electrolysis of water is also disclosed. The method includes providing a photoanode comprised of hematite, doping a surface of the electrode with at least one of nickel, cobalt and manganese, and electrically coupling a cathode to the photoanode, the cathode being configured for immersion in the water. The electrode surface may be doped with nickel. The electrode surface may be doped with cobalt. The electrode may be bulk doped with at least one of cobalt and nickel to enhance light absorption. The electrode may be bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport. The electrode surface may be doped with manganese. An aqueous solution may surround the photoanode and a cathode, the photoanode being configured to generate holes upon light absorption and the cathode being configured to emit electrons to the aqueous solution. A voltage source may be electrically coupled between the photoanode and the cathode.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a slab model of O-terminated Fe₂O₃ (0001): (a) (1×1) slab with 23 atoms per unit cell and (b) (2×2) slab with 92 atoms per unit cell;

FIGS. 2a-2f show models of optimized geometries of the O-terminated Fe₂O₃ (0001) surfaces with different coverages of H atoms;

FIG. 3a is a schematic illustration of the water oxidation reaction pathway on hematite showing optimized structures for all intermediates under vacuum;

FIG. 3b are diagrams of optimized hematite geometries with one explicit layer of H₂O (normal Bader charges: Fe +1.8; O −1.2; H+0.6);

FIG. 4 is a set of graphs showing projected densities of states (PDOS, n(E)) for pure and doped fully hydroxylated (1×1) Fe₂O₃ (0001) surfaces under vacuum;

FIG. 5 is a set of graphs showing the cumulative free energies of reactions (ΔG) for the pure and doped fully hydroxylated (1×1) Fe₂O₃ (0001) slabs under vacuum at different applied potentials;

FIG. 6a is a graph showing the binding energies of *OOH versus binding energies of *OH for the pure and doped fully hydroxylated (1×1) Fe₂O₃ (0001) surfaces under vacuum, with different U−J values for different dopants;

FIG. 6b is a graph showing the negative of the reaction potentials (−φ_(rx)) versus the binding energy differences of ΔG_(*O)−ΔG_(*OH);

FIG. 7a is a graph showing ΔG_(*O)−ΔG_(*OH) for slabs with different dopants;

FIG. 7b is a graph showing Bader charges of Ti, Mn, Co, Ni, and Si dopants and Fe at the same cation substitution site for pure and F doped surfaces;

FIG. 7c is a graph showing average Bader charges for *O and *OOH for the O anions in orange circles in FIG. 2;

FIG. 7d is a graph showing the valence band maximum for each slab with different dopants, under vacuum or in solvent; and

FIG. 8 is a block diagram of a photochemical cell including a photoanode constructed in accordance with the disclosure herein.

DETAILED DESCRIPTION OF THE INVENTION

Solar energy is a promising resource to help satisfy a fast growing global energy demand. Photoelectrochemical reactions can harvest solar energy by using sunlight to provide energy for endoergic chemical reactions, which in turn create reaction products that store chemical energy. The water splitting reaction, H₂O→H₂+O₂ (E⁰=−1.23 V), produces H₂ energy carriers, which can be used as a fuel itself or as a feedstock to produce liquid fuels. Water splitting requires not only energy input but also photoelectrocatalysts to accelerate the reaction. Hematite (α-Fe₂O₃, “α-” is omitted henceforth) has shown promise as a photocatalytic anode material. It has an indirect optical band gap of 1.9-2.2 eV which can absorb approximately 40% of the solar spectrum. It is cheap, abundant, nontoxic, and stable against corrosion. Its valence band and conduction band alignments permit water oxidation to produce oxygen, but it cannot form hydrogen without an applied voltage. Ti-doped hematite surfaces modified by exposure to a CoF₃ solution can shift the conduction band position so that an external bias is not required to generate hydrogen from water. This offers the promise of full water splitting (as opposed to just oxidation).

Hematite has some shortcomings, however, including low conductivity, a small optical absorption coefficient and fast electron-hole recombination rates. Consequently, improving the efficiency of hematite as a photoanode is desirable. N-type doping with Ti, Si, Ge, Zr, etc., may increase carrier concentrations and hence conductivity. Nanostructuring may shorten hole diffusion pathways and reduce electron-hole recombination. Surface modifications with cocatalysts or doping may improve reaction kinetics and reduce overpotentials. By incorporating these strategies, a water oxidation photocurrent of >3 mA/cm² was achieved using nanostructured hematite with an IrO₂ cocatalyst at an applied potential of +1.23 V versus the reversible hydrogen electrode under standard solar illumination conditions.

Hematite has a corundum lattice structure, with lattice constants a=5.035 Å and c=13.747 Å. Below the Néel temperature (TN=963 K), Fe₂O₃ is antiferromagnetic with weak ferromagnetism. The high-spin d⁵ Fe₃+ cations within one bilayer in the (0001) planes are ferromagnetically coupled to each other while antiferromagnetically coupled to the adjacent Fe bilayers. The two natural growth faces of hematite are the (0001) and the (0112) surfaces. Experimentally, both surfaces have been characterized under ultrahigh vacuum (UHV) and when in contact with water. Theoretically, the surface energies of the two surfaces under vacuum are similar, for example the (0001) surface is ˜0.1 J/m² less stable. The water oxidation reaction on the (0001) surface was examined and provides some understanding the redox surface chemistry of hematite. The termination of the (0001) surface is less complicated with fewer reconstructions than other surfaces. The disclosure herein is also relevant to related surface chemistry on the hematite (0112) surface and hematite polycrystalline surfaces such as those present on actual photoanodes.

Under UHV conditions, the single-layer Fe-terminated (0001) surface, which is stoichiometric and nonpolar, has been suggested to be the most stable by X-ray photoelectron diffraction and scanning tunneling microscopy (STM) experiments. Coexistence of the single-layer Fe-terminated surface and the O-terminated surface was observed by STM and low-energy electron diffraction (LEED) under an oxygen pressure of 10⁻⁴-10⁻¹ mbar. This coexistence was also predicted for certain oxygen partial pressures by full-potential linearized augmented plane wave density functional theory (DFT) calculations within the generalized gradient approximation (GGA) for exchange-correlation (XC). DFT-GGA calculations using projector augmented wave (PAW) potentials predicted that at a constant oxygen partial pressure of 0.2 bar, the most stable Fe₂O₃ (0001) surface below 500 K is the O-terminated surface. Because self-interaction errors (SIEs) inherent in standard Kohn-Sham DFT are large for localized Fe 3d electrons in Fe₂O₃, standard DFT incorrectly predicts narrow band gaps for bulk hematite and overestimates the interlayer spacings in both hematite bulk and surface structures. The DFT+U method, which includes exact intra-atomic exchange energy, has been proposed and successfully applied to strongly correlated materials to correct for the SIEs. Therefore, the above conclusions derived from DFT calculations may change if the more physically correct DFT+U theory is employed, as disclosed herein.

Water adsorption on the Fe2O3 (0001) surface has been experimentally characterized with various surface science techniques. In one study using X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy, Auger, and temperature programmed desorption (TPD), only ice condensation was observed on the stoichiometric surface at 175-220 K, while sputtered surfaces containing oxygen vacancies and concomitantly reduced Fe2+ ions chemisorb water strongly. Another study (on hydrated and hydroxylated hematite (0001) surfaces using XPS, scanning force microscopy (SFM), scanning electron microscopy (SEM), X-ray diffraction, and LEED) found adsorption and dissociation of H₂O were restricted to the top monolayer of the surfaces under ambient conditions. Another study using XPS for water adsorption on hematite (0001) near ambient conditions observed hydroxylation of only the topmost surface layer before water molecule adsorption. Another study was directed at the hydrated hematite (0001) surface at room temperature with a nearly-water-saturated He atmosphere using crystal truncation rod (CTR) diffraction and DFT-GGA calculations. Spacings of the terminating Fe and O layers were measured by CTR. Identifications of the terminations were made by comparing the measured spacings to those predicted by DFT and taking into account the thermodynamic stabilities of different terminations predicted by DFT. It has been suggested that two different hydroxylated domains coexist: one domain corresponds to a full hydroxylation of the single-layer Fe-terminated surface ((HO)₃—Fe—(HO)₃—Fe—R, where “R” represents the remaining layers in the bulk), and another domain is a fully hydroxylated O-terminated surface ((HO)₃—Fe—Fe—R) resulting from removal of a Fe(OH)₃ species from the first structure. Since DFT-GGA overestimates the spacings of hematite as already discussed above, the identifications based on comparing experimental data to DFT-GGA values should be viewed with caution.

Theoretically, water adsorption and hydroxylation of hematite surfaces have been studied by both atomistic simulations and DFT. According to one classical potential simulation, the structure with Fe(OH)₃ dissociating from the surface was 0.82 J/m² more stable than the structure with Fe(OH)₃ attached to the surface, implying desorption of Fe(OH)₃. DFT-GGA studies of Fe-terminated or defective hematite (0001) surfaces predicted that defective surfaces with Fe-adatoms or vacancies are more reactive toward H₂O. Theoretical studies detailing water oxidation mechanisms on hematite (0001) surfaces do not appear to be available.

Since the (HO)₃—Fe—(HO)₃—Fe—R domains might gradually evolve to (HO)₃—Fe—Fe—R after Fe(OH)₃ dissociates, this disclosure encompasses the surface chemistry of the hematite (0001) surface with the (HO)₃—Fe—Fe—R model termination. This disclosure also encompasses doping effects on the surface chemistry. For cation substitutions, several first-row transition metals (Ti, Mn, Co, and Ni) are considered. These first-row transition metal cations have similar ionic radii to Fe, but they have different numbers of 3d electrons, giving rise to different stable oxidation states. Si doping is also tested because it is commonly used to increase electron conductivity for n-doped hematite. For anion substitutions, F doping is tested by substituting it in for a terminating O. Unlike the terminating O in the hydroxylated surfaces, the terminating F anions do not bond to any H atoms since they are monovalent and only interact with a surface Fe atom.

Water Oxidation Reaction

The following reaction mechanism scheme is used to identify fundamental aspects of water splitting reactions, in particular water oxidation.

H₂O+*→*OH₂  A:

*OH₂→*OH+H⁺ +e ⁻  B:

*OH→*O+H⁺ +e ⁻  C:

H₂O+*O→*OOH+H⁺ +e ⁻  D:

*OOH→O₂+*+H⁺ +e ⁻  E:

The lone “*” represents a surface with one O vacancy site in the topmost layer. The symbols “*OH₂”, “*OH”, “*O”, and “*OOH” represent the surface with the corresponding chemisorbed species residing in the O vacancy site. The mechanism involves four oxidation steps (steps B-E), each of which results in a proton ejected into the electrolyte that will eventually meet a transferring electron at the cathode.

Starting with step A, H₂O first adsorbs onto the surface O vacancy site. The *OH₂ species then undergoes two subsequent oxidation reactions to form *O. Another oxidation step allows *O to react with another water molecule to form the *OOH intermediate. In the last oxidation, O₂ is released from the *OOH. The energy of H⁺+e⁻ is obtained implicitly by referencing it to the energy of H₂ using the standard hydrogen electrode (SHE, 1/2H₂→H⁺+e⁻, at pH=0, p=1 atm, T=298 K). Applying an external bias φ on the proton-coupled electron transfer processes in reactions B-E is accounted for by including a −e·φ term in their reaction free energies. For example, when φ=0 at standard conditions, the free energy of reaction C is the same as the free energy of the reaction *OH→*O+1/2H₂. Other electrochemical models explicitly simulate electrostatic responses to a constant field, or they generate an electric field via charged slabs and then compensate the extra charges with a uniform charge compensating background. In theoretical studies on water oxidation and oxygen reduction on Pt (111), these three models gave similar results. In this disclosure, the first and simplest model is adopted, which has also been applied to examine water oxidation on other metal oxide surfaces. Deviations from the standard pH=0 condition can be treated by adding a −kT ln10·pH correction, where k is the Boltzmann constant. Zero point energy (ZPE) and entropic contributions are also calculated or taken from standard tables (see Computational Details section). Enthalpy changes due to temperature increasing from 0 K→298 K are expected to be small and are normally neglected. Therefore, the reaction free energies are calculated as follows:

ΔG_(A)=E(*OH₂)−E(*)−E_(H) ₂ _(O)+(ΔZPE−TΔS)_(A)  (1)

ΔG_(B)=E(*OH)−E(*OH₂)+1/2E_(H) ₂ +(ΔZPE−TΔS)_(B) −e·φ  (2)

ΔG_(C)=E(*O)−E(*OH)+1/2E_(H) ₂ +(ΔZPE−TΔS)_(C) −e·φ  (3)

ΔG_(D)=E(*OOH)−E(*O)−E_(H) ₂ _(O)+1/2E_(H) ₂ +(ΔZPE−TΔS)_(D) −e·φ  (4)

ΔG_(E)=E(*)−E(*OOH)+E_(O) ₂ +1/2E_(H) ₂ +(ΔZPE−TΔS)_(E) −e·φ  (5),

E_(H) ₂ _(O), E_(H) ₂ , and E_(O) ₂ are the calculated energies for the isolated gaseous molecules H₂O, H₂, and O₂, respectively. Since ΔG_(A) is not an oxidative process, it does not depend on φ. Following Nørskov et al., the reaction potential, φ_(rx) is defined as the potential that makes all individual voltage-dependent steps (reactions B-E) have ΔG values ≦0. Therefore, φ_(rx) is equal to the most positive value among ΔG_(B), ΔG_(C), ΔG_(D), and ΔG_(E). The effective binding energies of O, OH, and OOH species at the surface O vacancy site, are calculated as:

ΔG_(*O)=E(*O)−E(*)−E_(H) ₂ _(O)+E_(H) ₂ ±ΔZPE−TΔS  (6)

ΔG_(*OH)=E(*OH)−E(*)−E_(H) ₂ _(O)+1/2E_(H) ₂ +ΔZPE−TΔS  (7)

ΔG_(*OOH)=E(*OOH)−E(*)−2E_(H) ₂ _(O)+3/2E_(H) ₂ +ΔZPE−TΔS  (8)

Lastly, the (average) H adsorption energy on the O-terminated surface is evaluated as:

G_(ad)=[E(O-terminated slab+nH)−E(O-terminated slab)−(n/2)E_(H) ₂ ]/n+ΔZPE−TΔS  (9),

Where n is the number of H atoms adsorbed onto the O-terminated surface.

Computational Models

The VASP program (version 5.2) was used for all calculations. The Perdew, Burke, and Ernzerhof (PBE) GGA exchange-correlation (XC) functional was employed. All-electron frozen core PAW potentials were used for the ion-electron terms (“ion” refers to a nucleus screened by its core electrons). Spin-polarized DFT+U theory was used to properly describe the antiferromagnetism of hematite and to correct the DFT SIEs for strongly correlated electrons in the first-row transition metal ions. The efficacy of this theory is evident for our purposes, as it has been shown to predict, e.g., more accurate redox potentials and oxidation energies of transition metal oxides than standard DFT. The rotationally-invariant DFT+U formalism was used as proposed by Dudarev et al. and implemented by Bengone et al. DFT+U predictions can depend on the value used for U−J, the one parameter in the theory, which represents the spherically averaged intra-atomic Coulomb minus exchange energy of the localized (here d) electrons that suffer the most from SIE. Rather than fit this parameter to match experiment as is frequently done, a fully ab initio value of U−J=4.3 eV was used for Fe, as derived for Fe³⁺ in Fe₂O₃ using a size-converged electrostatically-embedded cluster model within unrestricted Hartree-Fock theory. Our previous work using the ab initio derived U−J value (4.3 eV) for hematite showed that DFT+U predicts ground state structures and ground and excited state electronic properties of bulk hematite in very good agreement with experiments, in contrast to DFT alone. The DFT+U method using U−J=4.3 eV was validated in studies of the two lowest-energy surfaces of hematite. In this disclosure, two scenarios of U−J values were tested for the other first-row transition metals as dopants. In one case, the same U−J=4.3 eV was used for all the transition metals, so as to not artificially bias the 3d electron occupations among different transition metal cations. In the other case, the U−J was derived from experiments or from ab initio calculations (5.0 eV for Ti⁴⁺, 3.5 eV for Mn²⁺, 4.0 eV for Co³⁺, and 3.8 eV for Ni²⁺). Oxygen- and hydrogen-containing species were treated with standard DFT-PBE, since they do not exhibit much SIE; DFT-PBE describes molecular thermochemistry moderately accurately, with a mean unsigned error of 0.17 eV for alkyl bond dissociation energies (ABDE4 database).

The hexagonal unit cell of pure hematite was fully optimized at the PBE+4.3 (shorthand notation for using the PBE XC functional and U−J=4.3 eV) level, leading to predicted lattice vectors a=5.10 Å and c=13.92 Å, both of which are within 1% of the experimental values of a=5.04 Å and c=13.75 Å. (1×1) and (2×2) slab models of four stoichiometric units (˜9.3 Å thick, see FIG. 1) were built from the optimized bulk crystal structure. These two slabs of different lateral sizes are used to evaluate the dependence of reaction energetics on different concentrations of surface reaction sites (1/3 ML in the (1×1) slab compared to 1/12 ML in the (2×2) slab). Given the complex nature of a hematite electrode surface under hydrating conditions (due to polycrystalline facets, vacancies, and hydroxylation), the actual surface is expected to have more rather than less reactive sites. Thus, it is believed that the (1×1) slab that represents a higher concentration of reactive sites is more likely to be representative of the actual reaction conditions. Reactive species were introduced on both sides of the slab so the slab had no net dipole moment. In subsequent structural optimizations of the periodic slabs, the lateral lattice vectors were held fixed, while the ion positions were allowed to relax. A vacuum layer at least 10 Å thick (measured from wherever the slab or the water molecules end) was used to isolate slabs from their periodic images. Bader charges were calculated by integrating electron densities within zero flux surfaces around nuclei, and are converged to within 0.1 e compared to a grid 1.5 times denser along each lattice vector. The valence band maximum (VBM) was evaluated by referencing the energies of the highest occupied bands in the optimized slabs to the electrostatic potential energy in the vacuum region.

FIG. 1 shows the O-terminated Fe₂O₃ (0001) slab models of: (a) (1×1) slab with 23 atoms per unit cell and (b) (2×2) slab with 92 atoms per unit cell. O is depicted in red and Fe in grey. The ions for cation and anion substitutions are colored blue and purple, respectively. Only cation substitution was tested for the (2×2) slab.

Zero point energy (ZPE) and entropic contributions are presented for individual species in Table 1 and for individual reactions or binding energies in Table 2. The ZPE corrections were obtained from vibrational frequencies derived from Hessians calculated from finite differences of analytic gradients on single molecules in vacuum or adsorbates on (1×1) pure hematite slab models. The ZPE corrections calculated by Valdés et al. using DFT-GGA for related reactive species on the rutile TiO₂ (110) surface are included in Table 1 for comparison. The ZPE corrections calculated for reactive species on the Fe₂O₃ (0001) surface are very close to those for the TiO₂ (110) surface, with differences ≦0.07 eV. This similarity suggests that the vibrational frequencies of O—O and O—H bonds do not change significantly for different metal oxide substrates.

The entropic contributions for gaseous molecules are taken from standard thermodynamics tables. The entropic contributions to the total energy of a water molecule in solution is evaluated as the entropic contribution to the energy of a gas phase water molecule minus the condensation energy from gas to liquid for water at 298.15 K. This scheme enables us to physically model the absolute energy of a water molecule in liquid phase including solvation and standard state corrections. Entropic contributions from absorbed species on the surfaces are small, so they are usually omitted, as disclosed herein. For H adsorption, ΔZPE values in Equation (9) for different coverages of H are calculated to be close to 0.18 eV with deviations <0.01 eV. Since the entropic contributions from slabs with H adsorption are omitted, the −TΔS term in Equation (9) is 0.20 eV (one half of that for the H₂ molecule, see Table 1). Therefore, the ΔZPE−TΔS term in Equation (9) is set to 0.38 eV.

Table 1 shows the entropic energy contributions (T=298.15 K) and zero-point energy (ZPE) corrections for gaseous and adsorbed molecules and reactive species on hematite (0001).

TABLE 1 TS [eV] ZPE [eV] ZPE for TiO₂ [eV]⁵⁴ H_(2(g)) 0.40 0.27 0.27 O_(2(g)) 0.63 0.10 0.10 H₂O_((l)) 0.67 0.57 0.56 *O 0 0.04 0.05 *OH 0 0.37 0.35 *OOH 0 0.48 0.41 *OH₂ 0 0.67 0.70

Table 2 shows the entropic energy contributions (T=298.15 K) and ZPE corrections for reaction steps A-E and adsorbate binding energies, ΔG_(adsorbate). Values in parentheses for reactions A and E have a water molecule from the water layer bound to the O vacancy site in the otherwise clean “*” species, effectively making this intermediate an *OH₂ species (see bottom of FIG. 3b ).

ΔZPE-TΔS* [eV] Reaction A 0.77 (0.10) Reaction B −0.37  Reaction C −0.39  Reaction D 0.47 Reaction E −1.08 (−0.41) ΔG*_(O) 0.01 ΔG*_(OH) 0.40 ΔG*_(OOH) 0.48

Results

A) H adsorption on the O-terminated Fe2O3 (0001) surface

FIG. 2a-2f show models of optimized geometries of the O-terminated Fe₂O₃ (0001) surfaces with different coverages of H atoms. For each coverage, the lowest-energy structure is shown on the left. The unit cell size, number of H atoms, and coverage of H atoms is listed above each figure. “ML” means monolayer. The average H adsorption energy is given below each figure. FIGS. 2a-2f depict O in red, Fe in grey, and H in pink. This color scheme is used throughout.

Equilibrium structures were obtained for the fully hydroxylated Fe₂O₃ (0001) surface via H adsorption on the O-terminated Fe₂O₃ (0001) surface. The H atoms adsorbed onto this surface form terminating OH— groups that can adopt different orientations in which the H lies nearly within the O planes (e.g., FIG. 2(a)-i) or on top of the O anions (FIG. 2(a)-ii). Initially, the slabs with adsorbed H were built by adding H atoms manually to the slab. Depending on the starting geometry, the optimized structures varied in total energies, and the H atoms relaxed into different and seemingly arbitrary positions on the two sides of the slab. To systematically investigate the energetics of H adsorption and obtain minimum energy structures, a two-dimensional 7×7 grid of points on the (1×1) slab was used as initial positions for the adsorbed H atoms. The grid spacing is sufficiently dense (a distance of ˜0.73 Å between nearby points) to sample important positions on the surface, such as those on top of O anions and those at equal distances to adjacent O anions. The (1×1) slab (four stoichiometric units thick) is thick enough so that scanning along different H positions on one side of the slab does not influence the bonding of the H on the other side of the slab. Furthermore, although the entire slab itself does not have internal mirror symmetry, the atoms comprising the terminating O layers and their nearest Fe bilayers at each slab surface are nearly symmetric to each other (FIG. 2(a)). This means that H atoms aligned on opposite sides of the slab encounter almost the same bonding potential, meaning scans for both sides of the slab can proceed simultaneously. For the first scan, H atoms were added to opposite sides of the slab at one of the 7×7 grid points (at starting positions 0.8 Å away from the terminating O layers). The structures were then fully optimized for all 49 points. The lowest energy structure was then used in subsequent scans at higher coverage adding H atoms to each side of the new slabs in the same manner as before. Since the outermost atoms terminating the slabs are now H atoms, the starting positions for the subsequent, higher coverage PES scans are closer (0.5 Å away from the terminating atoms) to prevent the newly added H from being too far away from the outermost O layers. Following this procedure, the lowest-energy structures were obtained with up to four H atoms on each side of the slab (4/3 monolayer (ML), corresponding to 4 H atoms over 3 O anions in each terminating layer). Due to steric repulsion, ion relaxations from a (1×1) slab with five H atoms on each side resulted in water desorption, so H coverages >4/3 ML were not considered further.

B) Water oxidation reactions on the fully hydroxylated Fe2O3 (0001) surface

The minimum energy structures obtained by optimizing O-terminated slabs with different H coverages (as described above) are used as *O, *OH, and *OH₂ intermediates. The initial structures for *OOH and “*” were built manually starting from the optimized slabs at 2/3 ML H-coverage and then fully relaxed to find minima. The reaction pathway intermediates and the Bader charges for their surface ions are displayed in FIG. 3a . Here, water oxidation is illustrated as a continuous catalytic cycle. Starting at the top right, the reactant of reaction A, “*”, has one O vacancy in the terminating O layer. As a result, the Fe cation in the orange circle closest to the O vacancy is less ionic with less positive charge than normal (charges deviating from bulk values are shown in orange). In reaction A, one water molecule is adsorbed onto the surface at the O vacancy site, forming *OH₂. Since the water molecule is charge-neutral, the Fe cation remains in its lower oxidation state. In reaction B, one proton and one electron leave the surface (in a real system, the proton to the electrolyte and the electron into the hematite bulk crystal and out to an external circuit), producing the bulk-like fully hydroxylated Fe₂O₃ (0001) surface without any unusual Bader charges. In reaction C, the surface undergoes another oxidative process with another proton and electron removed. According to Bader analysis, the resulting hole resides on the deprotonated O anion. In reaction D, the *OOH product is formed by addition of water and loss of a proton and an electron, with both O anions in the —OOH group having less negative charge than the rest of the O anions. In reaction E, one O₂ molecule is released along with one proton and one electron.

FIG. 3a is a schematic illustration of the water oxidation reaction pathway on hematite showing optimized structures for all intermediates under vacuum. The terminating ions with unusual Bader charges are highlighted with orange circles, and their values reported below each figure in orange. Cumulative free energies of reactions (ΔG₂₉₈, normalized to the formation of one oxygen molecule) are plotted in the center of the reaction cycle. The “O” under x-axis represents the state consisting of the hematite surface containing one oxygen vacancy plus two water molecules in the liquid state. Line segments connect the adjacent reactions. For example, the line segment A-B illustrates the free energy for reaction B. The optimized geometries of reactive intermediates with a water overlayer are shown in FIG. 3b . For clarity, the reaction intermediates are illustrated on one side of the slab even though our models consider reactions on both sides of the slab. Normal Bader charges for Fe and O are derived from hematite bulk calculations. Normal Bader charges for H are derived from the *OH species, which exhibits hematite bulk-like geometry and electronic structure.

The cumulative reaction free energies (ΔG₂₉₈) for the proposed reactions steps are plotted in the center of FIG. 3a and given in Table 3 below. The gas phase energetics were analyzed first. With no applied external potential (φ=0 V), the cumulative ΔG₂₉₈ for all reactions is 4.43 eV, the DFT-GGA-PBE calculated water splitting reaction energy (2H₂O_((l))->O_(2(g))+2H_(2(g))). The predicted electrochemical reaction potential is then 1.11 V (4.43 eV/4e=1.11 V), a value in reasonable agreement with measured water splitting reaction potential of 1.23 V. The most endoergic step is reaction C. At an external potential φ of 1.11 V, the overall ΔG₂₉₈ for the reaction is zero. At this applied potential, the only endoergic steps are C and D. Recall that since reaction A does not involve an oxidation step, it is independent of φ. Increasing the applied potential further to φ_(rx)=1.82 V causes the ΔG₂₉₈ values of all electrochemical reactions (B−E) to be ≦0. The lower limit of the overpotential is then approximated as the difference between this 1.82 V value and the calculated water reaction potential of 1.11 V, which is equal to 0.71 V. Since the overpotential is a consequence of electrochemical kinetic barriers, it is appropriate to use kinetic schemes incorporating potential-dependent reaction barriers to obtain overpotentials. However, such barriers are challenging to calculate from first principles, and lower bounds to the overpotential provided by this simpler thermodynamic analysis has been demonstrated to satisfactorily predict experimental overpotentials for other electrocatalytic reactions.

Solvent effects are considered by adding a water overlayer (consisting of three water molecules for the (1×1) slab) on both sides of the slab. Earlier studies by Rossmeisl, et al. considered multiple layers of water to simulate the interface between an electrolyte and an electrified Pt (111) surface, and they found a single water layer capably described the variation of potential through the interface, suggesting that for flat surfaces such as the basal plane of hematite, a monolayer of water may be sufficient to capture both electrostatics and H bonding interactions. The initial geometries of the water layer are chosen manually, and they were built to maximize hydrogen bonding between the water layer and the surface O(H) species to assess the maximum perturbation caused by the water layer. The final optimized geometries are shown in FIG. 3 b.

The cumulative ΔG₂₉₈ for reactions with a monolayer of water on top is also plotted in FIG. 3a in orange. The lines connecting reactions A to D under vacuum conditions and with the H₂O monolayer are nearly parallel, implying nearly the same ΔG₂₉₈ for the individual reaction steps B, C, and D. Indeed, this solvation model mainly affects reactions A and E. As previously stated, when the surface with the O vacancy (*) is in contact with the water layer, a water molecule chemisorbs into the oxygen vacancy. This reduces the ΔG₂₉₈ for reaction A by 0.35 eV and increases the ΔG₂₉₈ for reaction E by 0.25 eV. The reaction potential φ_(rx) with the water layer is 1.88 V, only 0.06 V higher than the case under vacuum. As discussed in the Computational details section, it is believed that this model for water oxidation (using the (1×1) hydroxylated hematite slab with 1/3 ML reactive sites with an additional overlayer of water molecules) is most representative of experimental conditions. The overpotential of 0.77 V predicted is in reasonable agreement with the 0.5-0.6 V range measured for hematite photoanodes.

The ΔG₂₉₈s for the individual water oxidation reaction steps on the (1×1) and (2×2) slabs are provided in Table 3 below. The (1×1) slab (with 1/3 ML reactive sites) and the (2×2) slab (with 1/12 ML reactive sites) provide a measure of the reaction energy dependence on surface reactive site concentrations. The ΔG₂₉₈s for the (2×2) slab under vacuum are comparable to those for the (1×1) slab under vacuum, with differences ≦0.26 eV. The overall reaction potential for the (2×2) slab under vacuum is 0.2 V higher than the one for the (1×1) slab under vacuum. The similarity suggests that the reaction on the surface is fairly localized and exhibits only a small coverage dependence.

TABLE 3 (1 × 1) (2 × 2) 1/3 ML reactive sites 1/12 ML reactive sites Vacuum With H₂O Vacuum ΔG₂₉₈(A)  0.05 (−0.72) −0.20 (−0.30)  0.19 (−0.58) ΔG₂₉₈(B) −0.03 (0.34)  −0.07 (0.30)  −0.16 (0.22)  ΔG₂₉₈(C)

ΔG₂₉₈(D) 1.69 (1.22) 1.77 (1.30) 1.43 (0.96) ΔG₂₉₈(E) 0.90 (1.98) 1.05 (1.46) 0.95 (2.03) φ_(rx) 1.82 (2.21) 1.88 (2.27) 2.02 (2.41)

Table 3 shows the free energies of reactions (ΔG₂₉₈, in eV) without external bias (φ=0) and reaction potentials (φ_(rx), in V) for water oxidation on the fully hydroxylated, pure Fe₂O₃ (0001) surface. The numbers in parentheses are reaction energies omitting ZPE and entropic corrections. The most positive reaction energies within each column (equal to φ_(rx)) are in bold italic. The coverages refer to the concentration of oxygen vacancies at each surface.

C) Water oxidation reactions on the fully hydroxylated Fe2O3 (0001) surface with dopants

Table 4 (below) presents the reaction free energies and reaction potentials for water oxidation on the doped, fully hydroxylated hematite (0001) surfaces under vacuum and explicitly solvated conditions. The cation or anion dopants are bonded directly or positioned adjacent to the reaction site (see FIG. 1 and the Computational Models section above for more details). Unlike Table 3, only ΔG₂₉₈ values are reported with ZPE and entropic corrections. The reaction energies without ZPE and entropic corrections can be derived using corrections listed in Table 2. The results from the (1×1) slab models were analyzed first. In vacuum and employing the U−J values appropriate for different dopants discussed earlier, the φ_(rx) values for doped surfaces follow the ordering: Ni<Co<F<Mn<Si<Ti. The φ_(rx) values for Ni- and Co-doped surfaces are smaller than for a pure hematite surface. The Ti-doped surface has the largest φ_(rx), which is 1.45 V higher than for the pure hematite surface. When all dopants have the same U−J=4.3 eV as Fe, the above trend still holds. The ΔG₂₉₈ and φ_(rx) are similar in the two cases (using U−J values appropriate for individual dopants or same U−J=4.3 eV for all) and have a largest difference of 0.18 eV for ΔG₂₉₈ and 0.18 V for φ_(rx).

Table 4 also shows results from the (2×2) slab model under vacuum, employing different U−J values appropriate for different dopants. These data correspond to lowering the dopant concentration from 1/2 in the Fe bilayer of the (1×1) slab to 1/8 in the Fe bilayer of the (2×2) slab, as well as lowering the concentration of reactive sites from 1/3 to 1/12 ML. The predictions exhibit only a small dependence on the concentrations of dopants or reactive sites, with a largest difference of 0.26 eV for ΔG₂₉₈ and 0.12 V for φ_(rx). Therefore, similar to what is found for pure hematite in the previous section, the reaction is quite spatially localized and most sensitive to changes at adjacent sites.

The dopant effects resulting from the model employing appropriately different U−J values was also analyzed. Including one layer of water has a similar effect on doped surfaces as with pure hematite (Table 4). The φ_(rx) changes less than 0.1 V in all cases except for Si and F, which increase by 0.15 V and 0.28 V, respectively. To test the dependence of φ_(rx) on dopant concentrations, results for Ti, Mn, Co, Ni, and Si doping in the (2×2) slab models are also presented in Table 4. Calculations on F doping did not consistently converge properly for the larger (2×2) supercell, and therefore they are not reported.

Dopants retain similar charges in the (1×1) and (2×2) slabs in all cases except Ti. The latter can have either a +4 or a +3 charge when near the *OH and *OOH species at the lower coverage afforded by the (2×2) slab. When Ti has a +4 charge, a nearby Fe³⁺ cation is reduced to Fe²⁺ (just as for Ti doping in the (1×1) slab, vide infra). When Ti has a +3 charge, all the Fe cations have +3 charges. The *OH (or *OOH) with a nearby Ti³⁺ is higher in energy by 0.21 (or 0.08) eV than that with a nearby Ti⁴⁺, resulting in a 0.08 V difference in φ_(rx) between the Ti⁴⁺/Fe²⁺ and Ti³⁺/Fe³⁺ scenarios. Since the energy difference between these two cases depends on the U−J values used for Fe and Ti. The results for both (2×2) slab scenarios are shown in Table 4. Overall, predictions from (2×2) slabs are very similar to those of the (1×1) slabs, with largest differences being 0.26 eV for individual ΔG₂₉₈ values and only 0.12 V for φ_(rx). These small differences suggest that the water oxidation reaction on hematite surface depends primarily on the local chemical environment and does not drastically change with the dopant concentration. This conclusion should also apply to F doping.

TABLE 4 Dopant Ti Mn Co Ni Si F (1 × 1) ⅓ ML reactive sites - vacuum U-J [eV] 5.0 3.5 4.0 3.8 — — ΔG₂₉₈ (A) −0.08 0.04 0.07 0.00 0.44 −0.10 ΔG₂₉₈ (B) −0.38 0.37 0.75 0.99 −0.40 −0.02 ΔG₂₉₈ (C) 0.23 1.00

1.66 0.51

ΔG₂₉₈ (D)

1.61

1.56 ΔG₂₉₈ (E) 1.39 0.54 0.26 0.11 0.97 0.92 φ_(rx) 3.27 2.49 1.74 1.67 2.92 2.08 U-J [eV] 4.3 — — ΔG₂₉₈ (A) −0.05 0.02 0.06 −0.01 — — ΔG₂₉₈ (B) −0.53 0.54 0.85 1.08 — — ΔG₂₉₈ (C) 0.20 1.18

— — ΔG₂₉₈ (D)

1.59 1.61 — — ΔG₂₉₈ (E) 1.53 0.38 0.16 0.03 — — φ_(rx) 3.29 2.31 1.77 1.73 — — (1 × 1) ⅓ ML reactive sites - with H₂O U-J [eV] 5.0 3.5 4.0 3.8 — — ΔG₂₉₈ (A) −0.16 −0.16 −0.23 −0.27 −0.20 −0.21 ΔG₂₉₈ (B) −0.44 0.23 0.82 1.11 −0.65 −0.04 ΔG₂₉₈ (C) 0.35 1.08

0.58

ΔG₂₉₈ (D)

1.71 1.73

1.28 ΔG₂₉₈ (E) 1.36 0.72 0.33 0.11 1.63 1.04 φ_(rx) 3.32 2.57 1.80 1.75 3.07 2.36 (2 × 2) 1/12 ML reactive sites - vacuum U-J [eV] 5.0 3.5 4.0 3.8 — — ΔG₂₉₈ (A) −0.13 (−0.13) 0.15 0.17 0.11 0.32 — ΔG₂₉₈ (B) −0.44 (−0.24) 0.19 0.67 0.92 −0.66 — ΔG₂₉₈ (C) 0.25 (0.04) 1.06

0.61 — ΔG₂₉₈ (D)

1.63 1.64

— ΔG₂₉₈ (E) 1.45 (1.37) 0.67 0.26 0.09 1.22 — φ_(rx) 3.30 (3.38) 2.37 1.70 1.67 2.94 —

Table 4 shows the free energies of reactions (ΔG₂₉₈, in eV) without external bias (φ=0) and reaction potentials (φ_(rx), in V) for the water oxidation reaction on the doped fully hydroxylated (1×1) and (2×2) Fe₂O₃ (0001) surfaces. The most positive reaction energies within each column (equal to φ_(rx)) are in bold italic. Ti doping can occur in two different ways with the lower coverage (2×2) slab: values outside of parentheses are for the Ti⁴⁺/Fe²⁺ scenario that exists also for the higher coverage (1×1) slab, and values within parentheses are for the Ti³⁺/Fe³⁺ scenario that only occurs at the lower coverage.

Table 5 below reports the Bader charges and magnetic moments of dopants placed as nearest neighbors to the reactive O vacancy sites in the (1×1) slabs to discern their maximum effect. The charges and magnetic moments of Fe in the pure hematite surface are nearly identical to those of F doping and have a maximum difference of 0.1 in charge or 0.1μ_(B) in magnetic moment. The changes in charges of cation dopants for different surface reaction intermediates follow similar trends to what was found above for the pure hematite surface, but they are smaller in magnitude for Ti, Co, and Ni. The charges on the dopants in the * and *OH₂ species are smaller than the charges on the dopants with the other three reactive species present. Si dopants are an exception to this, however. Here, the charge on Si remains +3.1 throughout the catalytic reaction cycle, while O anions become more negatively charged compared to O anions in pure or other cation-doped hematite surfaces due to Si being electropositive.

FIG. 4 is a set of graphs showing projected densities of states (PDOS, n(E)) for pure and doped fully hydroxylated (1×1) Fe₂O₃ (0001) surfaces under vacuum. Positive values represent majority spin DOS whereas negative values represent minority spin DOS. The DOS are shifted so that the Fermi level is set to zero, with occupied states at negative energies E(eV).

The oxidation states and electronic configurations of the dopants were analyzed by combining information extracted from Bader charges, magnetic moments, and projected densities of states (PDOS). Since the fully hydroxylated surface (*OH) is the most bulk-like, the PDOS of the pure and doped hematite slabs containing the *OH species (FIG. 4) are analyzed. In pure hematite, the Fe³⁺ cations are in high spin d⁵ states (recall that first-row transition metals first give away their 4s electrons upon ionization, followed by ionization of their 3d electrons). The occupied states below the Fermi energy are of mixed Fe 3d and O 2p character, while the majority of Fe 3d states have energies below ˜−6 eV. For both Ti- and Si-doped hematite, one minority Fe 3d peak appears right below the Fermi energy. This peak suggests the existence of Fe²⁺ cations with one minority spin 3d electron, which result from cation substitution by Ti⁴⁺ or Si⁴⁺. The higher oxidation states of Ti and Si compared to other cations are evident from the Bader charges of Ti and Si in Table 5. A Co dopant can adopt oxidation states of either +2 or +3. Different initial magnetic moments for Co ions were tested; calculations converged to two possible configurations for the 3d electrons on Co, namely, the high spin and low spin cases. The spin state species with the lowest energy for reaction energy calculations was adopted. In the presence of *OH, the PDOS of Co has nearly symmetric majority and minority occupied 3d states, which, along with its 0.1μ_(B) magnetic moment, implies that Co is in the +3 oxidation state of low spin d⁶. Co's magnetic moment of 2.7μ_(B) in the presence of * and *OH₂ suggests that for these species Co prefers a high spin d⁷ electronic configuration with a +2 oxidation state. The PDOS of Ni shows more occupied majority states than minority states, and both are partially filled. The PDOS, together with the 0.8 μ_(B) magnetic moment for Ni, suggests that Ni in the presence of *OH has a low spin d⁷ electronic configuration with a +3 oxidation state. The magnetic moment of ˜1.6μ_(B) in * and *OH₂ suggests that Ni has a high spin d⁸ electronic configuration with a +2 oxidation state when these species are present. However, the charges of Co and Ni in Table 5 do not vary significantly, and all are smaller than that of Fe. The magnetic moment derived from spin density differences was considered to be a more sensitive measure of electron density around the cation. The Bader charges change little because the electron being added or removed is shared between Co/Ni and O, implying covalent character in Co—O and Ni—O bonds and intermediate charges between +2 and +3 for Co and Ni. For Mn, the similar Bader charges for Mn and Fe suggests that Mn is in the +2 oxidation state in the presence of * and *OH₂, and in the +3 oxidation state in the presence of *OH, *O, and *OOH. From the PDOS of Mn in the presence of *OH, the majority Mn 3d states are only partially filled, with unoccupied majority states appearing near the conduction band minimum. Along with a magnetic moment of 3.8μ_(B), this implies that Mn is in +3 oxidation state in the presence of *OH. These charge assignments for Ti, Mn, Co, and Ni agree with previous work by Velev et al. on a transition-metal-doped 30-atom unit cell of hematite using the local density approximation (LDA) +U method.

TABLE 5 Dopant Ti Mn Co Ni Si F U-J [eV] 5.0 3.5 4.0 3.8 — — Reaction Intermediate μ_(Ti) μ_(Mn) μ_(Co) μ_(Ni) μ_(Si) q_(Fe)/ μ_(Fe) q_(Ti) [μ_(B)] q_(Mn) [μ_(B)] q_(Co) [μ_(B)] q_(Ni) [μ_(B)] q_(Si) [μ_(B)] q_(F) [μ_(B)] * 2.0 0.9 1.5 4.5 1.2 2.7 1.2 1.6 1.4/−0.8 3.7 *OH₂ 2.1 0.9 1.5 4.6 1.3 2.7 1.2 1.7 1.4/−0.8 3.7 *OH 2.3 0.1 1.8 3.8 1.3 0.1 1.3 0.8 3.1 0.0 1.9/−0.7 4.3 *O 2.3 0.0 1.9 3.0 1.4 0.8 1.4 0.0 1.8/−0.7 3.6 *OOH 2.3 0.1 1.7 3.8 1.3 0.0 1.3 0.9 1.8/−0.7 4.2

Table 5 shows the Bader charges (q) and magnetic moments (a, in absolute values) of the dopants in the fully hydroxylated (1×1) Fe₂O₃ (0001) surfaces under vacuum. For F doping, the charges and magnetic moments of the Fe in the cation substitution sites are given.

FIG. 5 is a set of graphs showing the cumulative free energies of reactions (AG) for the pure and doped fully hydroxylated (1×1) Fe₂O₃ (0001) slabs under vacuum at different applied potentials. Different U−J values are used for different first-row transition metal elements.

The effects of using different dopants were also analyzed. The cumulative ΔG₂₉₈s for the case under vacuum with different U−J values for different dopants are plotted in FIG. 5 for four different external potentials. From the plots of φ=1.11 V and φ=2.00 V, the ΔG₂₉₈ values for reactions C and D show different signs for different dopants. At φ=1.11 V using pure or Co-, Ni-, or F-doped hematite, reactions C and D are the two most endoergic steps with positive ΔG_(C) and ΔG_(D). At 0=1.11 V using Ti, Mn, and Si doping, the most endoergic step is reaction D, while all other ΔG₂₉₈ values are slightly positive or are negative. Co or Ni doping each give rise to the lowest φ_(rx) and are unique among the other dopants as they exhibit linear energy changes from reactions B to D, such that ΔG_(C) and ΔG_(D) are both positive at φ=1.11 V and both negative at φ=2.00 V. This means reactions C and D are important steps for determining φ_(rx). Recall that reaction C corresponds to removing a proton and electron from *OH to form *O, and reaction D corresponds to *O reacting with water to form *OOH. Characterizing these three different species, *OH, *O, and *OOH is discussed below.

FIG. 6a is a graph showing the binding energies of *OOH versus binding energies of *OH for the pure and doped fully hydroxylated (1×1) Fe₂O₃ (0001) surfaces under vacuum, with different U−J values for different dopants. The linear fit is constrained to have a slope of 1. FIG. 6b is a graph showing the negative of the reaction potentials (−φ_(rx)) versus the binding energy differences of ΔG_(*O)−ΔG_(*OH). The orange (black) curve represents the results with (without) ZPE and entropic corrections.

Scaling relationships among binding energies of *OH, *O, and *OOH have been proposed from studying various transition metal oxide surfaces. For example, the differences in binding energies between *OH and *OOH are constant for a series of transition metal oxides. FIG. 6a plots the binding energy of *OOH (ΔG_(*OOH) in Equation (8)) versus that of *OH (ΔG_(*OH) in Equation (7)) with (in orange) and without (in black) ZPE and entropic corrections. Following Man et al.'s approach, linear fits are obtained by constraining the slope to be 1. The best-fit line with an R² value of 0.989 shows the proposed scaling relationship for *OOH and *OH also holds for pure or doped hematite surfaces. Since the key steps determining reaction potentials are the reactions C and D, the reaction potential with ZPE and entropic corrections follows

$(10)\begin{matrix} {\varphi_{rx} = {{\max \left( {{\Delta \; G_{C}},{\Delta \; G_{D}}} \right)}/e}} \\ {= {{\max \left\lbrack {\left( {{\Delta \; G_{*_{O}}} - {\Delta \; G_{*_{OH}}}} \right),\left( {{\Delta \; G_{*_{OOH}}} - {\Delta \; G_{*_{O}}}} \right)} \right\rbrack}/e}} \\ {= {\max {\left\{ {\left( {{\Delta \; G_{*_{O}}} - {\Delta \; G_{*_{OH}}}} \right),\left\lbrack {\left( {{\Delta \; G_{*_{OOH}}} - {\Delta \; G_{*_{OH}}}} \right) - \left( {{\Delta \; G_{*_{O}}} - {\Delta \; G_{*_{OH}}}} \right)} \right\rbrack} \right\}/e}}} \\ {{= {\max {\left\{ {\left( {{\Delta \; G_{*_{O}}} - {\Delta \; G_{*_{OH}}}} \right),\left\lbrack {3.464 - \left( {{\Delta \; G_{*_{O}}} - {\Delta \; G_{*_{OH}}}} \right)} \right\rbrack} \right\}/e}}},} \end{matrix}$

Where 3.464 is the intercept from the linear fitting of the orange curve in FIG. 6a . The second line of Equation (10) can be derived from Equations (3)-(4) and (6)-(8). According to this scaling relationship, the closer ΔG_(*O)−ΔG_(*OH) is with respect to 3.464/2=1.732 eV, the smaller the reaction potential, φ_(rx). This is confirmed by the plot of −φ_(rx) versus ΔG_(*O)−ΔG_(*OH) in FIG. 6b . Practically at the peak of the orange volcano curve is the case for Ni doping, located near ΔG_(*O)−ΔG_(*OH)=1.7 eV. The maximum expected activity is predicted because Ni doping provides the optimal relative binding strengths of *OH and *OOH. Including ZPE and entropic corrections adds different constants to the values of ΔG_(*O), ΔG_(*OH), and ΔG_(*OOH) (see Table 2). Comparing the black and orange curves in FIG. 6, these corrections shift both the peak positions of the volcano curves and the relative positions of dopants on the curves. These corrections make a qualitative difference in our predictions; in general, ZPE and entropic corrections to quantum mechanical energies at 0 K should always be added to model experimental conditions at finite temperature. In the literature these corrections are usually accounted for, but they are sometimes omitted when several varieties of oxide surfaces are under investigation. Based on the orange volcano curve in FIG. 6b , since the φ_(rx) for pure hematite lies close to the peak position of the volcano curve, only modest improvement can be expected over pure hematite.

FIG. 7 is a set of graphs showing various properties of the intermediate species in the water oxidation reaction on the pure (“Fe”) and doped fully hydroxylated (1×1) Fe₂O₃ (0001) surfaces under vacuum or in solvent, using different U−J values for different first-row transition metal dopants. FIG. 7a shows ΔG_(*O)−ΔG_(*OH) for slabs with different dopants. FIG. 7b shows Bader charges of Ti, Mn, Co, Ni, and Si dopants and Fe at the same cation substitution site for pure and F doped surfaces. FIG. 7c shows average Bader charges for *O and *OOH for the O anions in orange circles in FIG. 2. FIG. 7d shows the valence band maximum for each slab with different dopants, under vacuum or in solvent.

To further understand why different dopants affect ΔG_(*O)ΔG_(*OH) values, we analyze various properties of the reactive species. In FIG. 7, ΔG_(*O)ΔG_(*OH) is plotted against each specific dopant (or “Fe” in the case of pure hematite). It is clear that the ΔG_(*O)ΔG_(*OH) values are inversely related to the Bader charges of the transition metals and the VBM of the doped slabs, i.e., the larger the Bader charges of the transition metal cations (or the higher the VBM of the doped slabs), the smaller the ΔG_(*O)−ΔG_(*OH). The VBM values are less negative when more positively charged dopants are near the surface because such dopants draw out electrons from the bulk material making it easier to remove an electron from the surface. The VBM for the F doped slab is the most negative because the F atom is negatively charged and suppresses electrons coming from the bulk. In contrast, ΔG_(*O)−ΔG_(*OH) values correlate well with the Bader charges of the circled O anions in *O and *OOH (FIG. 3). These are more positive than the normal Bader charges of O, indicating probable hole localization on these O anions. Hole localization on O makes sense during the water oxidation reaction, where the oxidation states of O change from −2 to 0. Dopants that are more positively charged than Fe favor formation of *O on the surface (reaction C) because they help stabilize a more negatively charged O anion formed upon deprotonation. However, that more negatively charged O anion makes *OOH formation (reaction D) unfavorable, consistent with the relation that shows the tradeoff between reactions C and D:

ΔG_(*OOH)−ΔG_(*OH)=(ΔF_(*OOH)−ΔG_(*O))+(ΔG_(*O)−ΔG_(*OH))=ΔG_(D)+ΔG_(C)=3.464

(see equation within FIG. 6(a) and Equation (10)).

On the other hand, when the dopants are less positively charged than Fe, the O anions are less negatively charged. This favors *OOH formation but not *O formation. Therefore, it is believed that the most energetically favorable pathway requires moderate propensity for hole localization on the active O anions. The balanced bonding from Ni doping therefore gives the smallest reaction potential.

D) Perspectives on Photoelectrocatalysis—Model

Developing efficient photoelectrocatalysts requires optimizing various properties (e.g., band gaps, band edge character and alignments, electron/hole conductivity and lifetime, and reaction thermodynamics and kinetics). The current study focuses on reaction thermodynamics only. Water oxidation reaction steps are simulated here at the periodic DFT+U level by referencing to the SHE to avoid explicit modeling of proton release into water and electron injection into the semiconductor. Referencing to the SHE greatly simplifies the computation and has been successfully demonstrated in previous electrochemical modeling. The model we adopt also does not account for photoexcited holes within hematite. However, Valdéz and Kroes reported a DFT study on TiO₂ showing that calculations using neutral clusters as reactive catalysts give very similar results as calculations on positively charged clusters with one hole. They also showed that these cluster calculations gave similar results as periodic DFT calculations. Physically, localized holes at the hematite surface should enhance water oxidation, thus charge neutral models should provide a theoretical upper bound for overpotential estimates based on thermodynamics. On the other hand, since kinetic barriers were not evaluated here, the estimated overpotentials based on thermodynamics are lower bound estimates for the measured overpotentials. These two counter factors compete, resulting in error cancellation to some degree. Experimentally, the overpotential for the hematite photoanode has most recently been estimated at 0.5-0.6 V. The overpotential calculated herein of 0.77 V for liquid phase reaction on a pure (1×1) hematite slab (denoting 1/3 ML reactive sites) is just slightly above that experimental range, showing this model's approximate predictive capacity. Lower reactive site (and dopant) coverages give slightly higher overpotentials, but these may be less representative of a typical hematite/water interface that likely contains significant concentrations of defects (vacancies, grain boundaries, etc.) that will promote reactive site formation.

Photoelectrocatalytic water oxidation on hematite starts with light absorption in the near surface region of hematite. The resulting electrons and holes in the hematite anode are then separated: electrons flow to the external circuit, while holes migrate to the surface and react with water. Previously, theoretical calculations on optical excitations of pure hematite using an electrostatically embedded cluster showed that a charge transfer excitation from O to Fe is much higher in energy than the Fe d-d transition. Since hole localization on O is necessary in the water oxidation reaction (O evolves from −2 to 0 charge), the unfavorable ligand to metal charge transfer (LMCT) may limit the hole concentration on O in undoped hematite photoanodes, which in turn reduces their efficiencies.

Doping can enhance the efficiency of photoelectrocatalysis on hematite through different means. In the light absorption process, introducing other cation elements with lower-lying LMCT excitation states in their oxide phases might increase photogenerated hole concentrations on O anions. Since mid-to-late first-row transition metal oxides are of mixed Mott-Hubbard and charge-transfer character, additional bulk doping of hematite with Co or Ni might promote O hole concentration via LMCT between Co/Ni and O centers. Moreover, surface modifications with different dopants will affect the VBM level of the hematite slabs. Specifically, Ti, Mn, or Si doping shifts the VBM to be less negative while F doping shifts the VBM to be more negative (FIG. 7d ). The VBM for Co or Ni doped slabs are largely unaffected by doping. Since the CBM position of hematite is below that needed for water reduction, it is desirable to shift the VBM and CBM of hematite to less negative values. Therefore, it is believed that bulk and/or surface modifications with Ti, Mn, or Si will lead to favorable VBM alignments while the CBM alignment needs to be further verified by characterizing band gap changes after the modifications. In terms of electron transport in doped hematite, our earlier theoretical work on electron transport suggested that Si is a more favorable bulk dopant than Ti in the low doping concentration limit. Therefore, it is believed that Si is a better bulk dopant than Ti to improve band alignment and electron transport in hematite photoanodes. On the other hand, it is believed that Ti or Si surface doping increases the water oxidation overpotential on hematite surfaces, with Ti surface doping giving the highest φ_(rx).

Lastly, as disclosed herein dopants adjacent to reaction sites change reaction thermodynamics. The presence of dopants can modulate the bonding strengths between the surface and the intermediate adsorbed species in the water oxidation reaction. According to the Sabatier principle, interactions between the catalysts and the adsorbates should be intermediate: neither too weak to adsorb the reactants nor too strong as to inhibit product leaving the catalyst. Among a series of dopants, Co and Ni are predicted as the most effective additives to reduce overpotentials because their less positive charge compared to Fe provides optimal binding strengths to the O, OH, and OOH adsorbates.

A review of measurements of photoelectrochemical properties of Ni-doped hematite by Liu, et al. reveals that Ni-doping leads to higher photocurrent densities for water oxidation compared to pure hematite samples. The improved performance of the Ni-doped hematite surface was attributed to increased conductivity and higher charge separation efficiency, but our work suggests additionally that the reaction thermodynamics is improved. An observed reduction of 0.05 V in the onset potential for Ni-doped samples further validates the disclosed effectiveness of Ni-doped hematite.

Photochemical Cell Structure

FIG. 8 is a block diagram of a photochemical cell 20 including a photoanode 22 constructed in accordance with the disclosure herein and a cathode 24. It should be understood that the photochemical cell 20 may be constructed using conventional materials as is well known to those skilled in the art. The photoanode 22 may be constructed using conventional techniques for water oxidation to evolve oxygen and generally includes hematite with Ni, Co and/or Mn doping as disclosed above. The cathode 24 may also be constructed using conventional materials. In a typical example, the cathode 24 is constructed using platinum and/or other materials that are catalytic for hydrogen reduction. In general, the photochemical cell 20 includes an electrolyte or aqueous solution 26 generally surrounding the photoanode 22 and a cathode 24. A light source, e.g., sunlight, is generally is directed at the photochemical cell 20 as shown by arrow 21. The photoanode 22 and cathode 24 are electrically connected as shown by reference number 28. The photochemical cell 20 may optionally include a voltage source 30 configured to oppose the overpotential. It should be understood that a variety of fabrication techniques may be used for example as disclosed in the article entitled Solar Water Splitting: Progress Using Hematite (a-Fe2O3) Photoelectrodes, Sivula et al., ChemSusChem 2011, 4, 432-449 (2011) which is incorporated herein in its entirety.

SUMMARY

Disclosed herein are ab initio DFT+U calculations to characterize the thermodynamics of water oxidation on the hematite (0001) surface. Our previous work demonstrated that extensions beyond standard DFT (i.e. ab initio DFT+U) must be employed to obtain accurate structures and electronic properties of hematite. In this disclosure, reaction potentials are calculated for water oxidation in both gas and liquid phases on a (1×1) hydroxylated hematite slab (1/3 ML reactive sites) and in the gas phase for a (2×2) slab (1/12 ML reactive sites). Since actual hematite electrode surfaces under hydrating conditions undoubtedly have a complex structure with polycrystalline facets, vacancies, and hydroxylation, it is believed that predictions based on the explicitly solvated, hydroxylated (1×1) slab that contains a higher concentration of reactive sites to be more representative of actual electrochemical conditions. This model gives a reaction potential φ_(rx), defined as the minimum potential that makes ΔG≦0 for all individual electrochemical steps, of 1.88 V, corresponding to an overpotential of 0.77 V. This calculated overpotential is in reasonable agreement with measured overpotentials of 0.5-0.6 V for hematite photoanodes.

Cation doping (Ti, Mn, Co, Ni, Si) was introduced by direct cation substitutions, and F doping was introduced by substituting an OH group on the fully hydroxylated surface. Including ZPE and entropic corrections shifts reaction energy levels, qualitatively changing the predictions of which dopants act to reduce the overpotential. By accounting for ZPE and entropic corrections and by using ab initio U−J values for the dopants, Co or Ni doping reduces the φ_(rx) of pure hematite by up to 0.15 V. In contrast, Ti, Mn, Si, and F doping increased the φ_(rx) beyond that of pure hematite, suggesting Co and Ni additions are candidates to improve the catalytic activity of pure hematite. The doping effects were analyzed by comparing charges of the dopants and active O anions as well as the binding energies of O, OH, and OOH adsorbates. Specifically, optimal binding of O, OH, and OOH reactive species is the key to reduce the reaction potential. Co or Ni, both with charges less positive than Fe, produce intermediately-charged O anions that best balance the binding strengths among O, OH, and OOH, yielding the smallest reaction potential.

Although features and elements are described above in particular combinations, each feature or element may be used alone without the other features and elements or in various combinations with or without other features and elements. 

1. A photoanode comprising an electrode at least partially formed of hematite and having a surface doped with at least one of nickel, cobalt and manganese, the electrode having a (0001) surface Fe bilayer doped with a concentration in the 1/8 to 1/2 range.
 2. The photoanode of claim 1, wherein the electrode surface is doped with nickel.
 3. The photoanode of claim 1, wherein the electrode surface is doped with cobalt.
 4. The photoanode of claim 1, wherein the electrode surface is doped with manganese.
 5. The photoanode of claim 1, wherein the electrode is bulk doped with at least one of cobalt and nickel to enhance light absorption.
 6. The photoanode of claim 1, wherein the electrode is bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport.
 7. The photoanode of claim 1, further comprising an aqueous solution surrounding the photoanode and a cathode, the photoanode being configured to generate holes upon light absorption and the cathode being configured to emit electrons to the aqueous solution.
 8. The photoanode of claim 7, further comprising a voltage source electrically coupled between the photoanode and the cathode.
 9. A photochemical cell configured for electrolysis of water, the photochemical cell comprising: a photoanode comprised of hematite and having a surface doped with at least one of nickel, cobalt and manganese configured for immersion in the water; and a cathode electrically coupled to the photoanode, the cathode being configured for immersion in the water.
 10. The photochemical cell of claim 9, wherein the electrode surface is doped with nickel.
 11. The photochemical cell of claim 9, wherein the electrode surface is doped with cobalt.
 12. The photochemical cell of claim 9, wherein the electrode surface is doped with manganese.
 13. The photochemical cell of claim 9, wherein the electrode is bulk doped with at least one of cobalt and nickel to enhance light absorption.
 14. The photochemical cell of claim 9, wherein the electrode is bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport.
 15. The photochemical cell of claim 9, wherein the photoanode is configured to generate holes upon light absorption and the cathode is configured to emit electrons to the water.
 16. The photochemical cell of claim 15, further comprising a voltage source electrically coupled between the photoanode and the cathode.
 17. A method of making a photoanode, the method comprising: providing an electrode at least partially formed of hematite; and doping a surface of the electrode with at least one of nickel, cobalt and manganese.
 18. The method of claim 17, wherein the electrode surface is doped with nickel.
 19. The method of claim 17, wherein the electrode surface is doped with cobalt.
 20. The method of claim 17, wherein the electrode surface is doped with manganese.
 21. The method of claim 17, wherein the electrode is bulk doped with at least one of cobalt and nickel to enhance light absorption.
 22. The method of claim 17, wherein the electrode is bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport.
 23. The method of claim 17, further comprising surrounding the photoanode and a cathode with an aqueous solution, the photoanode being configured to generate holes upon light absorption and the cathode being configured to emit electrons to the aqueous solution.
 24. The photoanode of claim 23, further comprising electrically coupling a voltage source between the photoanode and the cathode.
 25. A method of making a photochemical cell configured for electrolysis of water, the method comprising: providing a photoanode comprised of hematite; doping a surface of the electrode with at least one of nickel, cobalt and manganese; and electrically coupling a cathode to the photoanode, the cathode being configured for immersion in the water.
 26. The method of claim 25, wherein the electrode surface is doped with nickel.
 27. The method of claim 25, wherein the electrode surface is doped with cobalt.
 28. The method of claim 25, wherein the electrode surface is doped with manganese.
 29. The method of claim 25, wherein the electrode is bulk doped with at least one of cobalt and nickel to enhance light absorption.
 30. The method of claim 25, wherein the electrode is bulk doped with at least one of silicon and manganese to enhance band alignment and carrier transport. 